Modular algorithms for heterogeneous modal logics via multi-sorted coalgebra

Date

2011

Authors

Schroder, Lutz
Pattinson, Dirk

Journal Title

Journal ISSN

Volume Title

Publisher

Cambridge University Press

Abstract

State-based systems and modal logics for reasoning about them often heterogeneously combine a number of features such as non-determinism and probabilities. In this paper, we show that the combination of features can be reflected algorithmically, and we develop modular decision procedures for heterogeneous modal logics. The modularity is achieved by formalising the underlying state-based systems as multi-sorted coalgebras and associating both a logical and algorithmic description with a number of basic building blocks. Our main result is that logics arising as combinations of these building blocks can be decided in polynomial space provided this is also the case for the components. By instantiating the general framework to concrete cases, we obtain PSpace decision procedures for a wide variety of structurally different logics, describing, for example, Segala systems and games with uncertain information.

Description

Keywords

Keywords: Basic building block; Building blockes; Coalgebras; Decision procedure; Modal logic; Modular algorithms; Non-determinism; Polynomial space; State-based systems; Uncertain informations; Algorithms; Formal logic

Citation

Source

Mathematical Structures in Computer Science

Type

Journal article

Book Title

Entity type

Access Statement

License Rights

Restricted until

2037-12-31